The field \(g_\mu \)  plays a distinguished role in defining the state of quantum fields. The structure of the counterterms suggests the simplest form of the classical action for this field. Its Lagrangian density reads [1]}, [2]}, [3]}, [4]}
\(\mathcal {L}=-\frac{1}{4}f^2-\frac{1}{2}(\bar{\alpha }|\phi |^2+\bar{\beta }+\bar{\kappa } R)g^2-\frac{\bar{\gamma }}{4}g^4,\qquad \bar{\gamma }>0,\) 
